Find the area enclosed between the curves y = f(x) and y = g(x)
Don't forget, in order to find the area under a curve y=f(x) between two values x=a and x=b we integrate f(x) between a and b.Thus to find the area enclosed between two curves y=f(x) and y=g(x) we simply need to integrate (g(x)-f(x)), with the negative in front of whichever function has smaller values between a and b. We can go through an example to see how this works.Find the area enclosed between the curves y = x2 + 2x + 2 and y = -x2 +2x + 10.Equate the two and simplify to get a=-2, b=2.-x2 +2x + 10 is larger, so this is g(x) and we must integrate g(x) - f(x) = -2x2 + 8.This integration yields -2x3/3 + 8x, which when evaluated at a=-2, b=2 gives 64/3.
